One of the most important reactions in the fixation of nitrogen for agriculture is known as the Haber Process for making ammonia shown below.

$(\frac{1}{3})N_2+b{H}_{2}cN{H}_3$

a$)$ Balance to chemical equation.

$b=1$

$c=\frac{2}{3}$

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b$)$ Calculate the standard enthalpy of reaction at $298\mathrm{.}15K$ for the assigned stoichiometry. $(k\frac{J}{m}ol)$

$-30\mathrm{.}628198$

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c$)$ Calculate the Standard Gibbs energy of reaction at $298\mathrm{.}15K$ for the assigned stoichiometry. $(k\frac{J}{m}ol)$

$-10\mathrm{.}93474671$

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Be careful that the units on the Gibbs energy or reaction match with units on $R.$

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e$)$ Calculate $K_{a,690}$ at $690K$ using the short$-$cut van't Hoff equation.

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f$)$ Enter the equation for the equilibrium constant using partial pressures of the components in algebraic form. The variables you should use are pNH$3,$ pH$2,$ pN$2,$ are the partial

pressures of $N{H}_3,H_2,N_2$ respectively.

$K_a=$

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g$)$ Enter the equation for the equilibrium constant using total pressure and mole fractions. The variables you should use are $yN{H}_3,yH2,y{N}_2,$ for the mole fractions of $N{H}_3,H_2,N_2$

respectively and the total pressure, $P.$

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h$)$ Assuming that the moles fed into the reactor are $2$ of nitrogen and $4$ of hydrogen develop an algebraic equation for the total number of moles at reaction equilibrium using the

reaction coordinate. Use E for the reaction coordinate.

Total moles$=$

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i$)$ Now develop an algebraic equation for the mole fraction of $N{H}_3$ at equilibrium. Use $E$ for the reaction coordinate.

$y_{NH3}=$

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j$)$ Develop an algebraic equation for the mole fraction of $N_2$ at equilibrium. Use $E$ for the reaction coordinate.

$y_{N2}=$

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